CHICAGO – It’s difficult to nitpick an outing in which the opponent scored only one run in seven innings.

But White Sox starter Jake Peavy wasn’t satisfied with his performance Saturday against the Minnesota Twins despite a quality start that put his teammates in position for the win. However, the offense managed only one run off the Twins, a solo homer by Alejandro De Aza to lead off the first, in a 2-1 loss in 10 innings.

After the game, Peavy immediately suggested that had he not given up the one run with two outs in the third on Josh Willingham’s RBI single, “it would have saved us the game.” Yet it was because of Peavy’s ability to take advantage of a pitcher-friendly strike zone (nine strikeouts) and work around his four walks that the Sox and their meager offense even had a chance to pull out the win.

“I think that’s the first thing you think of is you hate wasting outings like that,” manager Robin Ventura said. “I think any time a guy pitches like that, it’s always one of those unfortunate things you don’t get him a win. He’s been pitching well enough to get a couple of wins out of it.”

The loss keeps the Sox (7-10) in fourth place in the AL Central after dropping eight of their past 11 games. Twins starting pitcher Vance Worley entered the game having allowed eight runs in his past 11 innings. Instead, he pitched like he was one of best starters in the league, holding the Sox to five hits in seven innings. Sox hitters failed to record an extra-base hit after De Aza’s homer in the first, and struck out 13 times compared to three walks.

“It was just a good pitchers’ duel,” Paul Konerko said. “I hate to waste an outing by Jake. … It would have been nice to get him a win, but we just couldn’t get anything going.”

For a team that’s trying to grind out wins, failing to take advantage of Peavy’s start is maddening. Although it took him 30 minutes to emerge in the locker room after the loss, Peavy suppressed any frustrations and refused to blame the offense for what should have been a win against a Twins team that isn’t exactly brimming with talent. The Sox had won 12 of their past 14 games against the Twins (7-7) before the offense no-showed.

“I’d rather it have been me than a [Jose] Quintana or [Chris] Sale or somebody that hasn’t been through it,” Peavy said. “I’ve really pitched through my whole career in tight ball games. If you look back at some of those years in San Diego, I didn’t have a whole lot of run support. I’m fine with it. I’m OK with pitching in tight ball games.”

Even though Peavy is used to pitching in such games, the Sox often have found themselves on the losing side of games he has started in the past year. In 2012, the Sox lost 17 of Peavy’s 32 starts, and 10 of those losses were in two-run games. However, with Sale on the mound, the Sox won two-thirds of his starts last year. The Sox can’t afford to blow great opportunities when one of their best starting pitchers is on the mound.

“Wins and losses on my fifth day are important to me,” Peavy said. “When you start a game your team loses, I don’t care how it happens, it’s not fun. I believe we’ll find a way. We went through some tough stretches last year. Hopefully, we can right the ship sooner than later.”

• Meghan Montemurro covers the White Sox and Cubs for Shaw Media. Write to her at mmontemurro@shawmedia.com. Read the Payoff Pitch blog at NWHerald.com and on Twitter @Sox_Insider and @InsideTheCubs.